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The results of a study of time optimal rendezvous in three dimensions with bounds on the rocket thrust and the available propellant are described. The equa¬tions of motion are linearized and Neustadt's method is used to solve the...
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The results of a study of time optimal rendezvous in three dimensions with bounds on the rocket thrust and the available propellant are described. The equa¬tions of motion are linearized and Neustadt's method is used to solve the two-point boundary value problem in the seven-dimensional state space. Three convergence acceleration schemes are studied. Fletcher and Powell's modification of Davidon's method was superior to Powell's method and a modified method of steepest ascent. Examples of terminal rendezvous paths are presented and discussed in terms of the magnitudes of the bounds on thrust and fuel. The dependence of terminal errors on initial measurement errors in position and velocity is also discussed.
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Pseudo-boolean (and general nonlinear integer) functions provide an extremely powerful modeling and solution tool in operations research and related areas. A large number of practical as well as purely theoretical decision problem...
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Pseudo-boolean (and general nonlinear integer) functions provide an extremely powerful modeling and solution tool in operations research and related areas. A large number of practical as well as purely theoretical decision problems can be easily represented and solved as optimization of a pseudo-boolean or general nonlinear integer function. In the framework of this project we have considered several stochastic extensions of classical combinatorial optimization problems that involve some type of nonlinearity, typically in the objective function. We have provided respective theoretical analysis and developed advanced solution approaches. In particular, we have investigated the following topics: (i) exact solution algorithms for broad classes of two-stage stochastic quadratic binary and general integer programming problems; (ii) approximation algorithms for solving a class of two- stage stochastic assignment problems; (iii) theoretical analysis of two-stage stochastic minimum s-t cut problems; (iv) exact solution algorithm for a class of stochastic bilevel knapsack problems; (v) exact solution algorithms for a class multiple-ratio fractional programming problems; and (vi) integer programming approach for solving a polyomino tiling problem with application in antenna design.
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It has long been known that barrier algorithms for constrained optimization canproduce a sequence of iterates converging to a critical point satisfying weak second-order necessary optimality conditions, when their inner iterations...
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It has long been known that barrier algorithms for constrained optimization canproduce a sequence of iterates converging to a critical point satisfying weak second-order necessary optimality conditions, when their inner iterations ensures that second-order necessary conditions hold at each barrier minimizer. The authors show that, despite this, strong second-order necessary conditions may fail to be attained at the limit, even if the barrier minimizers satisfy second-order sufficient optimality conditions.
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In this paper we consider the Hamiltonian formulation of the equations ofincompressible ideal fluid flow from the point of view of optimal control theory. The equations are compared to the finite symmetric rigid body analyzed earl...
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In this paper we consider the Hamiltonian formulation of the equations ofincompressible ideal fluid flow from the point of view of optimal control theory. The equations are compared to the finite symmetric rigid body analyzed earlier by the authors. We discuss various aspects of the Hamiltonian structure of the Euler equations and show in particular that the optimal control approach leads to a standard formulation of the Euler equations-the so-called impulse equations in the Lagrangian form. We discuss various other aspects of the Euler equations from a pedagogical point of view. We show that the Hamiltonian in the maximum principle is given by the pairing of the Eulerian impulse density with the velocity. We provide a comparative discussion of the flow equations in their Eulerian and Lagrangian form and describe how these forms occur naturally in the context of optimal control. We demonstrate that the extremal equations corresponding to the optimal control problem for the flow have a natural canonical symplectic structure.
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This work develops a global minimization framework for segmentation of high dimensional data into two classes. It combines recent convex optimization methods from imaging with recent graph based variational models for data segment...
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This work develops a global minimization framework for segmentation of high dimensional data into two classes. It combines recent convex optimization methods from imaging with recent graph based variational models for data segmentation. Two convex splitting algorithms are proposed, where graph-based PDE techniques are used to solve some of the subproblems. It is shown that global minimizers can be guaranteed for semi- supervised segmentation with two regions. If constraints on the volume of the regions are incorporated, global minimizers cannot be guaranteed, but can often be obtained in practice and otherwise be closely approximated. Experiments on benchmark data sets show that our models produce segmentation results that are comparable with or outperform the state-of-the-art algorithms. In particular, we perform a thorough comparison to recent MBO and phase field methods, and show the advantage of the algorithms proposed in this paper.
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